CANTON  Count on Cantor
One of the famous proofs of modern mathematics is Georg Cantor's demonstration that the set of rational numbers is enumerable. The proof works by using an explicit enumeration of rational numbers as shown in the diagram below.
1/1 1/2 1/3 1/4 1/5 ... 2/1 2/2 2/3 2/4 3/1 3/2 3/3 4/1 4/2 5/1
In the above diagram, the first term is 1/1, the second term is 1/2, the third term is 2/1, the fourth term is 3/1, the fifth term is 2/2, and so on.
Input
The input starts with a line containing a single integer t <= 20, the number of test cases. t test cases follow.
Then, it contains a single number per line.
Output
You are to write a program that will read a list of numbers in the range from 1 to 10^7 and will print for each number the corresponding term in Cantor's enumeration as given below.
Example
Input: 3 3 14 7 Output: TERM 3 IS 2/1 TERM 14 IS 2/4 TERM 7 IS 1/4
hide comments
parthendo:
20161006 21:32:26
Read CAREFULLY and it's AC ;) 

vdbhatt:
20160920 22:41:43
good problem... use penpaper 

jawad_cs:
20160912 02:07:26
Please help me...it is mentioned in the question that the 4th term is 3/1.....is it correct...i think it should be 1/3..it would form a pattern then 

rajat_bir2015:
20160830 22:38:35
plot the graph to get the pattern


nikunjsoni:
20160817 16:53:09
AC in first attemp :) time  0.00 

sharif ullah:
20160811 21:22:32
here number of test case is 20 .so precalculation may give TLE 

SidXDDD:
20160716 17:48:38
Last edit: 20160720 16:02:11 

Pikachu:
20160713 16:52:09
Last edit: 20160713 16:56:04 

epsilonalpha:
20160624 18:56:10
AC in first try, 0.06 seconds in Java. Just observe the pattern and the rest is very simple, no algorithm needed! 

rishabh_1997:
20160619 13:08:28
A very nice question... Just pick a paper & try to find the pattern

Added by:  ThanhVy Hua 
Date:  20050227 
Time limit:  5s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: NODEJS PERL 6 VB.net 
Resource:  ACM South Eastern European Region 2004 